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Simplifying (3x + -7) * 2 + -5(2x + 1)(x + -2) = -1x2 + -1[-1(3x + 1)] Reorder the terms: (-7 + 3x) * 2 + -5(2x + 1)(x + -2) = -1x2 + -1[-1(3x + 1)] Reorder the terms for easier multiplication: 2(-7 + 3x) + -5(2x + 1)(x + -2) = -1x2 + -1[-1(3x + 1)] (-7 * 2 + 3x * 2) + -5(2x + 1)(x + -2) = -1x2 + -1[-1(3x + 1)] (-14 + 6x) + -5(2x + 1)(x + -2) = -1x2 + -1[-1(3x + 1)] Reorder the terms: -14 + 6x + -5(1 + 2x)(x + -2) = -1x2 + -1[-1(3x + 1)] Reorder the terms: -14 + 6x + -5(1 + 2x)(-2 + x) = -1x2 + -1[-1(3x + 1)] Multiply (1 + 2x) * (-2 + x) -14 + 6x + -5(1(-2 + x) + 2x * (-2 + x)) = -1x2 + -1[-1(3x + 1)] -14 + 6x + -5((-2 * 1 + x * 1) + 2x * (-2 + x)) = -1x2 + -1[-1(3x + 1)] -14 + 6x + -5((-2 + 1x) + 2x * (-2 + x)) = -1x2 + -1[-1(3x + 1)] -14 + 6x + -5(-2 + 1x + (-2 * 2x + x * 2x)) = -1x2 + -1[-1(3x + 1)] -14 + 6x + -5(-2 + 1x + (-4x + 2x2)) = -1x2 + -1[-1(3x + 1)] Combine like terms: 1x + -4x = -3x -14 + 6x + -5(-2 + -3x + 2x2) = -1x2 + -1[-1(3x + 1)] -14 + 6x + (-2 * -5 + -3x * -5 + 2x2 * -5) = -1x2 + -1[-1(3x + 1)] -14 + 6x + (10 + 15x + -10x2) = -1x2 + -1[-1(3x + 1)] Reorder the terms: -14 + 10 + 6x + 15x + -10x2 = -1x2 + -1[-1(3x + 1)] Combine like terms: -14 + 10 = -4 -4 + 6x + 15x + -10x2 = -1x2 + -1[-1(3x + 1)] Combine like terms: 6x + 15x = 21x -4 + 21x + -10x2 = -1x2 + -1[-1(3x + 1)] Reorder the terms: -4 + 21x + -10x2 = -1x2 + -1[-1(1 + 3x)] -4 + 21x + -10x2 = -1x2 + -1[(1 * -1 + 3x * -1)] -4 + 21x + -10x2 = -1x2 + -1[(-1 + -3x)] -4 + 21x + -10x2 = -1x2 + [-1 * -1 + -3x * -1] -4 + 21x + -10x2 = -1x2 + [1 + 3x] Reorder the terms: -4 + 21x + -10x2 = 1 + 3x + -1x2 Solving -4 + 21x + -10x2 = 1 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: -4 + -1 + 21x + -3x + -10x2 + x2 = 1 + 3x + -1x2 + -1 + -3x + x2 Combine like terms: -4 + -1 = -5 -5 + 21x + -3x + -10x2 + x2 = 1 + 3x + -1x2 + -1 + -3x + x2 Combine like terms: 21x + -3x = 18x -5 + 18x + -10x2 + x2 = 1 + 3x + -1x2 + -1 + -3x + x2 Combine like terms: -10x2 + x2 = -9x2 -5 + 18x + -9x2 = 1 + 3x + -1x2 + -1 + -3x + x2 Reorder the terms: -5 + 18x + -9x2 = 1 + -1 + 3x + -3x + -1x2 + x2 Combine like terms: 1 + -1 = 0 -5 + 18x + -9x2 = 0 + 3x + -3x + -1x2 + x2 -5 + 18x + -9x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -5 + 18x + -9x2 = 0 + -1x2 + x2 -5 + 18x + -9x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -5 + 18x + -9x2 = 0 Factor a trinomial. (-5 + 3x)(1 + -3x) = 0Subproblem 1
Set the factor '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Divide each side by '3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {1.666666667, 0.3333333333}
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